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Course18.065 / 18.065134 lectures

Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Prof. Gilbert Strang · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

Lectures

Video Lectures

  1. Lecture 1: The Column Space of A Contains All Vectors Ax 53 min · Video
  2. Lecture 2: Multiplying and Factoring Matrices 49 min · Video
  3. Lecture 3: Orthonormal Columns in Q Give Q’Q = I 50 min · Video
  4. Lecture 4: Eigenvalues and Eigenvectors 49 min · Video
  5. Lecture 5: Positive Definite and Semidefinite Matrices 46 min · Video
  6. Lecture 6: Singular Value Decomposition (SVD) 54 min · Video
  7. Lecture 7: Eckart-Young: The Closest Rank k Matrix to A 48 min · Video
  8. Lecture 8: Norms of Vectors and Matrices 50 min · Video
  9. Lecture 9: Four Ways to Solve Least Squares Problems 50 min · Video
  10. Lecture 10: Survey of Difficulties with Ax = b 50 min · Video
  11. Lecture 11: Minimizing ‖x‖ Subject to Ax = b 51 min · Video
  12. Lecture 12: Computing Eigenvalues and Singular Values 50 min · Video
  13. Lecture 13: Randomized Matrix Multiplication 53 min · Video
  14. Lecture 14: Low Rank Changes in A and Its Inverse 51 min · Video
  15. Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt 51 min · Video
  16. Lecture 16: Derivatives of Inverse and Singular Values 44 min · Video
  17. Lecture 17: Rapidly Decreasing Singular Values 51 min · Video
  18. Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points 49 min · Video
  19. Lecture 19: Saddle Points Continued, Maxmin Principle 53 min · Video
  20. Lecture 20: Definitions and Inequalities 56 min · Video
  21. Lecture 21: Minimizing a Function Step by Step 54 min · Video
  22. Lecture 22: Gradient Descent: Downhill to a Minimum 53 min · Video
  23. Lecture 23: Accelerating Gradient Descent (Use Momentum) 50 min · Video
  24. Lecture 24: Linear Programming and Two-Person Games 54 min · Video
  25. Lecture 25: Stochastic Gradient Descent 54 min · Video
  26. Lecture 26: Structure of Neural Nets for Deep Learning YouTube
  27. Lecture 27: Backpropagation: Find Partial Derivatives 53 min · Video
  28. Lecture 30: Completing a Rank-One Matrix, Circulants! 50 min · Video
  29. Lecture 31: Eigenvectors of Circulant Matrices: Fourier Matrix 53 min · Video
  30. Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule 48 min · Video
  31. Lecture 33: Neural Nets and the Learning Function 57 min · Video
  32. Lecture 34: Distance Matrices, Procrustes Problem 30 min · Video
  33. Lecture 35: Finding Clusters in Graphs 35 min · Video
  34. Lecture 36: Alan Edelman and Julia Language 39 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Gilbert Strang
Term
Spring 2018
Level
Undergraduate
Language
English
Subjects
Mathematics, Computer science, Engineering
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Gilbert Strang. Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Spring 2018. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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